Generalized probability theories (GPTs [1]}, [2]}, [3]}, [4]}, [5]}) are a framework to infer as much as possible about a physical system without making assumptions about its inner workings (like the assumption that states can be represented as vectors in a Hilbert space). Instead, it is assumed that agents can implement and label a number of physical procedures, like preparations, transformations and, crucially, measurements. Note that the agents need not know the actual physical state prepared; in order to label a procedure, they only need to be confident that they can repeat it.
Indeed, the basic assumption behind GPT frameworks is that agents can extract significant measurement statistics (for example, by repeating a procedure many times). Hence, GPTs model outputs of measurements as random variables, and agents' knowledge of procedures as probability distributions.
